Edit to add again: Okay, I tried to start a New game but clicking past the movie that leads to the prison causes a CTD. I'm pretty screwed here.
By "clicking past the movie that leads to the prison" do you mean you're trying to skip the movie? Have you tried just letting it play thru without interrupting it?
If that doesn't help, have you tried uninstalling & re-installing the game? It sounds as if the game program files themelves might have been messed up in one of the crashes. I realize that is very painful, especially if you have a lot of mods installed (I do), but that happened to me, & it's what finally resolved my problems.
Like schijnn, I found that moving all but the last few savegames into a backup folder significantly improved stability & pretty much eliminated CTD's. His recommendation to save before going thru doors is a good one. In some places (the IC store being one of them), I did it every single time I went thru the door, both entering & leaving, as the game seems to be especially prone to crashing there. I do think the autosave has something to do with it ... see my earlier comments on that. It's been a while since I played, so I can't remember if you can turn autosave off or not, but if you can, that might be worth trying. Good luck!